Combining Philosophers

All the ideas for Anaxarchus, Bernard Bolzano and Paul Audi

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24 ideas

2. Reason / B. Laws of Thought / 1. Laws of Thought
7807 The laws of thought are true, but they are not the axioms of logic [Bolzano, by George/Van Evra]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
9987 An aggregate in which order does not matter I call a 'set' [Bolzano]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
9618 Bolzano wanted to reduce all of geometry to arithmetic [Bolzano, by Brown,JR]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10856 A truly infinite quantity does not need to be a variable [Bolzano]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
9830 Bolzano began the elimination of intuition, by proving something which seemed obvious [Bolzano, by Dummett]
7. Existence / C. Structure of Existence / 1. Grounding / a. Nature of grounding
17292 Avoid 'in virtue of' for grounding, since it might imply a reflexive relation such as identity [Audi,P]
17295 Ground relations depend on the properties [Audi,P]
17297 A ball's being spherical non-causally determines its power to roll [Audi,P]
17302 Ground is irreflexive, asymmetric, transitive, non-monotonic etc. [Audi,P]
17303 The best critique of grounding says it is actually either identity or elimination [Audi,P]
7. Existence / C. Structure of Existence / 1. Grounding / b. Relata of grounding
17294 Grounding is a singular relation between worldly facts [Audi,P]
17300 If grounding relates facts, properties must be included, as well as objects [Audi,P]
7. Existence / C. Structure of Existence / 1. Grounding / c. Grounding and explanation
17265 Philosophical proofs in mathematics establish truths, and also show their grounds [Bolzano, by Correia/Schnieder]
17296 We must accept grounding, for our important explanations [Audi,P]
7. Existence / C. Structure of Existence / 1. Grounding / d. Grounding and reduction
17301 Reduction is just identity, so the two things are the same fact, so reduction isn't grounding [Audi,P]
7. Existence / D. Theories of Reality / 8. Facts / b. Types of fact
17293 Worldly facts are obtaining states of affairs, with constituents; conceptual facts also depend on concepts [Audi,P]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
9185 Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved [Bolzano, by Dummett]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
3061 Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
17298 Two things being identical (like water and H2O) is not an explanation [Audi,P]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
17299 There are plenty of examples of non-causal explanation [Audi,P]
19. Language / D. Propositions / 1. Propositions
22276 Bolzano saw propositions as objective entities, existing independently of us [Bolzano, by Potter]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
17264 Propositions are abstract structures of concepts, ready for judgement or assertion [Bolzano, by Correia/Schnieder]
12232 A 'proposition' is the sense of a linguistic expression, and can be true or false [Bolzano]
19. Language / E. Analyticity / 2. Analytic Truths
12233 The ground of a pure conceptual truth is only in other conceptual truths [Bolzano]